No abstract

No abstract

A mi familia, la que toco y la que pienso; a mis amigos, distribuidos en diferentes lugares y momentos; y a Hanse, silenciosa pero siempre presente To my family, tangible and intangible; to my friends, spread over the space and time ... and to my cat, best roomate I can ask for If we are satisfied with things as they are, nothing will ever be discovered.

In some geological formations, borehole resistivity measurements can be simulated using a sequence of 1D models. By considering a 1D layered media, we can reduce the dimensionality of the problem from 3D to 1.5D via a Hankel transform. The resulting formulation is often solved via a semi-analytic method, mainly due to its high performance. However, semi-analytic methods have important limitations such as, for example, their inability to model piecewise linear variations on the resistivity. Herein, we develop a multi-scale finite element method (FEM) to solve the secondary field formulation. This numerical scheme overcomes the limitations of semi-analytic methods while still delivering high performance. We illustrate the performance of the method with numerical synthetic examples based on two symmetric logging-while-drilling (LWD) induction devices operating at 2 MHz and 500 KHz, respectively.